The use of seismic surveys is now fundamental in the search for oil and gas reservoirs in the earth. As is rudimentary in the art, seismic surveys are performed by imparting acoustic energy of a known amplitude and frequency pattern at one or more locations of the earth (either at a land surface or in a marine environment), and then detecting reflected and refracted acoustic energy at other locations. The delay time between the imparting of the acoustic energy at the source location and detection of the same wave at a receiver location is indicative of the depth at which a particular reflecting geological interface is located. The field of seismic data analysis is concerned with techniques for analyzing the detected acoustic energy to determine both the location and also the properties of various geological strata.
A known technique in the generation and analysis of conventional seismic surveys is referred to as amplitude-versus-offset ("AVO") analysis. According to the AVO approach, attributes of a subsurface interface are determined both from the normal-incidence amplitude of reflected seismic energy and also from the dependence of the detected seismic reflections on the angle of incidence of the energy. According to conventional AVO analysis, multiple seismic traces (i.e., time-domain signals at different detection locations) that include a signal from a common reflection point are collected; such a group of traces is commonly referred to as a common-depth point (CDP) gather. Typically, a series of common reflection points for the same source-receiver pairs underlie the same surface location at the midpoint between the source and receiver for multiple offsets; as such, this gather is also often referred to as a common midpoint (CMP) gather.
From the CDP (or CMP) gather, one may derive the amplitude R of a reflected seismic wave from an interface (i.e., the "target horizon") as a function of the angle of incidence .theta. from the normal according to the following relationship: EQU R(.theta.)=A+B sin.sup.2 .theta.
In this case, the coefficient A is the zero-offset response (also referred to as the AVO intercept), while the coefficient B is referred to as the AVO slope, or gradient, as it is representative of the rate of change of amplitude with the square of the angle of incidence.
For a given reflection event from a horizon between two geological formations, the values of A and B will depend upon the physical properties of the two formations. The well-known Zoeppritz equations provide closed form equations for R(.theta.) based upon the compressional velocities (V.sub.p), shear velocities (V.sub.s), and densities (.rho.) of the two formations at the reflecting interface. However, inversion of the Zoeppritz equations to solve for the elastic properties of the formations from reflection data is impractical, due to numerical complexity.
By way of further background, the calculation of theoretical values for A and B for isolated rock interfaces (i.e., at specific horizons) through the use of the linearized Zoeppritz equations and based upon typical values for compressional velocity, density and Poisson's ratio for the strata on either side of the interface of interest, is described in Swan, "Properties of direct AVO hydrocarbon indicators", Offset-dependent reflectivity--Theory and Practice of AVO analysis (Castagna, J. P. & Backus, M. M., eds., Soc. Expl. Geophys., 1993), pp. 78-92. As described therein, variations in the A and B values for particular interfaces from a theoretical A-versus-B trend line for the expected stratigraphic sequences can indicate the location of interfaces in the survey.
Typically, AVO seismic data analysis involves the derivation of so-called "indicators" from the A and B coefficients for reflection depth points in the survey. In order to convey phase information regarding the reflections, the A and B coefficient values as a function of time are frequently converted into complex, or analytical, traces by applying the Hilbert transform to the measured A and B values. A common AVO indicator is generated from such complex traces as the product of the complex AVO intercept value A with the complex conjugate of the AVO slope B; this indicator function thus has the form f(A,B)=AB*. Typically, the amplitude of the indicator function is plotted as a function of time in similar fashion as raw or stacked seismic traces, with each indicator trace associated with a surface location. Variations in the amplitude of the indicators over time can identify the location of geological interfaces, particularly those which correspond to formations potentially bearing oil and gas in producible quantities.
For example, conventional AVO seismic analysis begins with the acquisition of data for a two-dimensional or three-dimensional survey in the usual manner. Conventional seismic data processing is then performed, including such operations as multiple elimination, filtering, prestack migration (i.e., time-domain to depth transformation) and normal move-out (NMO) correction, followed by grouping the signals into CDP gathers. Conventional AVO analysis then performs a regression of the seismic signals in each gather to derive the A and B coefficient values at each depth point, typically through a least-squares fit of the seismic data versus the squared sine of the angle of incidence. Once the A and B coefficient values are determined for each depth in the survey area, indicators such as the product AB* may be plotted as a survey section over surface location and time (i.e., in CMP-time space), similarly as seismic survey sections of other types.
Certain indicators are known as reliable in identifying the location of potential oil and gas reservoirs. For example, the product AB* is known to indicate the presence of hydrocarbon bearing sands of the so-called "Class 3" type. Class 3 sands are relatively shallow formations, and have an acoustic impedance that is less than the acoustic impedance of a neighboring shale, which results in interfaces therebetween for which the A and B coefficients in AVO analysis are both strongly negative; the product AB* at such interfaces is thus a positive value of detectable amplitude, and is a reliable indicator of the presence of the Class 3 sand.
By way of further background, U.S. Pat. No. 5,661,617, filed Dec. 18,1995, entitled "Method and Apparatus for Detection of Sand Formations in Amplitude-Versus-Offset Seismic Surveys", assigned to Atlantic Richfield Company and incorporated herein by this reference, describes a new AVO indicator for common depth points based upon the value of the AVO intercept A and the deviation of the AVO gradient B from a trend line. The indicator described in this application has been found useful for distinguishing hydrocarbon sands from surrounding formations.
By way of still further background, copending application Ser. No. 08/614,744, pending, filed Mar. 13, 1996, entitled "Method and System for Detecting Hydrocarbon Reservoirs Using Amplitude-versus-Offset Analysis of Seismic Signals", assigned to Atlantic Richfield Company and incorporated herein by this reference, describes a new AVO indicator for common depth points based upon the rate of change of the product of the AVO intercept value and the AVO gradient value for the depth point under analysis, along the direction of a deviation vector of the AVO intercept value and the AVO gradient value from a background trend for depth points surrounding the depth point under analysis in time and space. This new indicator, referred to therein as the .DELTA.(AB*) indicator, has proven to be especially valuable in the detection of very deep gas-bearing sands, such sands commonly referred to as Class 1 and Class 2 sands.
Regardless of the particular indicator used in the AVO analysis, potential hydrocarbon reservoirs and interfaces thereof are identified by those locations in the survey for which the indicator value has a significant value. In each of the above cases, as is typical in the art, the AVO indicator is designed to have a large magnitude for depth points that differ, in a petrophysically interesting way, from the background. For example, the simple product indicator AB operates in this fashion, considering that the A and B coefficients are typically negatively correlated with one another at non-hydrocarbon-bearing locations; positive values of the product of the A and B coefficients thus indicate deviations from this negative correlation. Other indicators, including those described hereinabove, operate in a similar fashion to distinguish possible oil or gas bearing locations or interfaces from the background.
In the simple case, one may characterize the background as a best-fit straight line in the A-B plane, and calculate deviations of individual points from the trend line in differentiating hydrocarbon-bearing locations or interfaces from wet or dry formations. As described in the above-incorporated U.S. Pat. No. 5,661,617 and Ser. No. 08/614,744, pending and also in U.S. Pat. No. 5,515,335, filed Aug. 16, 1993, assigned to Atlantic Richfield Company and incorporated herein by this reference, several important statistical characteristics of the values of A and B for each depth point in a portion of a survey may be calculated, such characteristics including the root-mean-square (RMS) of the A and B coefficients, and also the correlation coefficient between A and B over the survey portion of interest. These statistical characteristics provide the analyst with a measurement of the spread of the A and B values in the background trend, from which a statistically adjusted value of the deviation of the AVO indicator for a given depth point from the background trend may be determined.
According to conventional techniques, the criteria used in identifying potential hydrocarbon reservoirs is simply the magnitude of the indicator value. For example, conventional systems display the value of the indicator for each depth point in a survey of common midpoint gathers by way of a color display, where the hue of each point corresponds to the value of the indicator according to a predefined scale. This approach provides the human analyst with a way of readily identifying interesting locations in the survey. This approach has been useful in identifying petrophysically interesting subsurface locations in those cases where the magnitude of the indicator is relatively large. However, heretofore there has been no objective criterion for selection of the indicator threshold, or of the color scale used in the display techniques. As a result, it has been observed in connection with the present invention that conventional AVO indicator analysis techniques are unable, in many cases, to distinguish depth points having a positive AVO indicator but which is not statistically distinct from the background trend (and thus not likely to be interesting to the analyst) from those depth points with positive indicators that are statistically distinct from the background trend. In other words, some depth points in the survey at non-hydrocarbon bearing locations (i.e., within the background trend) may have the same magnitude of AVO indicator as true hydrocarbon-bearing locations, if one considers only the indicator magnitude as the threshold criterion as is conventional in the art.
It is therefore an object of the invention to provide a method and system for analyzing AVO surveys so as to improve the accuracy of the AVO prediction.
It is a further object of the present invention to provide such a method and system that may be used with any one of several AVO indicators.
It is a further object of the present invention to provide such a method and system that may be implemented in an automated fashion.
Other objects and advantages of the present invention will be apparent to those of ordinary skill in the art having reference to the following specification together with its drawings.